Casimir torque in weak coupling

TL;DR

This paper investigates Casimir torque between planar objects in the weak-coupling limit, providing exact calculations that compare well with the proximity force approximation at small separations and exploring shape dependence.

Contribution

It offers the first exact weak-coupling calculations of Casimir torque between planar objects, clarifying the validity of the proximity force approximation.

Findings

Excellent agreement with proximity force approximation at small separations

Shape dependence diminishes when object size is comparable to separation

Results are relevant for conducting planar objects and experimental tests

Abstract

In this paper, dedicated to Johan H{\o}ye on the occasion of his 70th birthday, we examine manifestations of Casimir torque in the weak-coupling approximation, which allows exact calculations so that comparison with the universally applicable, but generally uncontrolled, proximity force approximation may be made. In particular, we examine Casimir energies between planar objects characterized by $\delta$-function potentials, and consider the torque that arises when angles between the objects are changed. The results agree very well with the proximity force approximation when the separation distance between the objects is small compared with their sizes. In the opposite limit, where the size of one object is comparable to the separation distance, the shape dependence starts becoming irrelevant. These calculations are illustrative of what to expect for the torques between, for example, conducting planar objects, which eventually should be amenable to both improved theoretical calculation and experimental verification.